Inverse Problems in Engineering Selection of Multiple Regularization Parameters in Local Ridge Regression Using Evolutionary Algorithms and Prediction Risk Optimization

This paper presents a new methodology for regularizing data-based predictive models. Traditional modeling using regression can produce unrepeatable, unstable, or noisy predictions when the inputs are highly correlated. Ridge regression is a regularization technique used to deal with those problems. A drawback of ridge regression is that it optimizes a single regularization parameter while the methodology presented in this paper optimizes several local regularization parameters that operate independently on each component. This method allows components with significant predictive power to be passed while components with low predictive power are damped. The optimal combination of regularization parameters are computed using an Evolutionary Strategy search technique with the objective function being a predictive error estimate. Examples are presented to demonstrate the advantages of this technique.